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fixed error in fix_nh1.tex

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git-svn-id: svn://svn.icms.temple.edu/lammps-ro/trunk@3981 f3b2605a-c512-4ea7-a41b-209d697bcdaa
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athomps
2010-04-12 18:00:21 +00:00
parent 6bd79b1c2e
commit f68adcfe2b
2 changed files with 11 additions and 14 deletions
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21
doc/Eqs/fix_nh1.tex
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@ -12,27 +12,24 @@
{\ensuremath{{\rm i}}} {\ensuremath{{\rm i}}}
$$ \begin{eqnarray*}
\exp \left(\iu{} L \Delta t \right) = \exp \left(\iu{} L \Delta t \right) &=&<EFBFBD>
\exp \left(\iu{} L_{\rm T\mhyphen baro} \frac{\Delta t}{2} \right) \exp \left(\iu{} L_{\rm T\mhyphen baro} \frac{\Delta t}{2} \right)
\exp \left(\iu{} L_{\rm T\mhyphen part} \frac{\Delta t}{2} \right) \exp \left(\iu{} L_{\rm T\mhyphen part} \frac{\Delta t}{2} \right)
\exp \left(\iu{} L_{\epsilon , 2} \frac{\Delta t}{2} \right) \exp \left(\iu{} L_{\epsilon , 2} \frac{\Delta t}{2} \right)
\exp \left(\iu{} L_{2}^{(2)} \frac{\Delta t}{2} \right) \exp \left(\iu{} L_{2}^{(2)} \frac{\Delta t}{2} \right) \\
$$ &&\times \left[
$$
\times \left[
\exp \left(\iu{} L_{2}^{(1)} \frac{\Delta t}{2n} \right) \exp \left(\iu{} L_{2}^{(1)} \frac{\Delta t}{2n} \right)
\exp \left(\iu{} L_{\epsilon , 1} \frac{\Delta t}{n} \right) \exp \left(\iu{} L_{\epsilon , 1} \frac{\Delta t}{n} \right)
\exp \left(\iu{} L_1 \frac{\Delta t}{n} \right) \exp \left(\iu{} L_1 \frac{\Delta t}{n} \right)
\exp \left(\iu{} L_{2}^{(1)} \frac{\Delta t}{2n} \right) \exp \left(\iu{} L_{2}^{(1)} \frac{\Delta t}{2n} \right)
\right]^n \right]^n \\
$$ &&\times
$$
\exp \left(\iu{} L_{2}^{(2)} \frac{\Delta t}{2} \right) \exp \left(\iu{} L_{2}^{(2)} \frac{\Delta t}{2} \right)
\exp \left(\iu{} L_{\epsilon , 2} \frac{\Delta t}{2} \right) \exp \left(\iu{} L_{\epsilon , 2} \frac{\Delta t}{2} \right)
\exp \left(\iu{} L_{\rm T\mhyphen part} \frac{\Delta t}{2} \right) \exp \left(\iu{} L_{\rm T\mhyphen part} \frac{\Delta t}{2} \right)
\exp \left(\iu{} L_{\rm T\mhyphen baro} \frac{\Delta t}{2} \right) \exp \left(\iu{} L_{\rm T\mhyphen baro} \frac{\Delta t}{2} \right) \\
+ \mathcal{O} \left(\Delta t^3 \right) &&+ \mathcal{O} \left(\Delta t^3 \right)
$$ \end{eqnarray*}
\end{document} \end{document}